Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 143 millimeters, and a standard deviation of 5. If a random sample of 47 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 0.2 millimeters? Round your answer to four decimal places

Answer 1

The probability that the sample mean would differ from the population mean by more than 0.2 millimeters is

1) Using Excel function = 0.3920

2) Using z table = 0.3936

The complete solution of above question are as below

The values provided in the above question are as below

Mean = = 143

Standard deviation = = 5

Sample size = = 47

We have to find the probability that the sample mean would differ from the population mean by more than 0.2 millimeters

-------(1)

We convert above   into using following formula

-----------(2)

Using equation (2) in equation (1) we get

We find above probability using following Excel function

(Round answer to four decimal places)

The probability that the sample mean would differ from the population mean by more than 0.2 millimeters is 0.3920

Or

We find above probability using z table of standard normal curve areas

We convert the above z to two decimal places, because in z table of standard normal curve areas the z value is available only two decimal places.

(Round answer to two decimal places)

We find above probability using z table of standard normal curve areas

The probability that the sample mean would differ from the population mean by more than 0.2 millimeters is 0.3936

Summary :-

The probability that the sample mean would differ from the population mean by more than 0.2 millimeters is

1) Using Excel function = 0.3920

2) Using z table = 0.3936